Novel Magnetic Field Dependence of the Coupling of Excitations between Two Fermion Fluids

We have observed a new magnetic field dependence to the thermal boundary resistance between liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and finely powdered silver particles. At a temperature of 1 mK we find the thermal boundary resistance to increase by nearly an order of magnitude as the magnetic field is raised from 0 to 200 mT. This behavior cannot be explained by conventional acoustic models of the heat conduction. By contrast, however, we observe no field dependence from 0.2 to 9.4 T, in strong contradiction to the behavior expected based on the recent conduction model of Perry et al.